Data Import，remove ‘Keshavarz4_urine’, ‘Keshavarz4_tissue’,
‘Hong8’, ‘Marotta23’ study due to large 95% CI
setwd("~/Desktop/meta analysis/BPA_cancer")
# load the data with strongest effect of OR
meta_data_s_remove <- read_excel("data.xlsx", sheet = "strong_or") %>%
janitor::clean_names() %>%
filter(!(auther %in% c('Keshavarz4_urine', 'Keshavarz4_tissue', 'Hong8', 'Marotta23')))
# load the data with average effect of OR
meta_data_a_remove <- read_excel("data.xlsx", sheet = "average_or") %>%
janitor::clean_names() %>%
filter(!(auther %in% c('Keshavarz4_urine', 'Keshavarz4_tissue', 'Hong8', 'Marotta23')))
# Calculate the log of odds ratios and their standard errors
# strong effect of OR
meta_data_s_remove <- meta_data_s_remove %>%
mutate(
log_odds_ratio = log(or),
lower_log =log(lower_ci),
upper_log = log(upper_ci),
se_log_odds_ratio = (upper_log - lower_log) / (2 * 1.96) # 1.96 is the Z value for 95% CI
)
# average OR
meta_data_a_remove <-meta_data_a_remove %>%
mutate(
log_odds_ratio = log(or),
lower_log =log(lower_ci),
upper_log = log(upper_ci),
se_log_odds_ratio = (upper_log - lower_log) / (2 * 1.96) # 1.96 is the Z value for 95% CI
)
Part 1, general meta analysis
# strong effect OR
meta_s_analysis_remove <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = meta_data_s_remove,
sm = "OR"
)
summary(meta_s_analysis_remove)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.9500 [0.7479; 1.2067] 5.2 7.2
## Morgan3 0.7600 [0.4471; 1.2917] 1.1 5.3
## Tse9_mult 1.8800 [1.2379; 2.8551] 1.7 6.0
## Loperz10_mult 2.3100 [1.4284; 3.7357] 1.3 5.6
## Trabert11 1.0400 [0.9172; 1.1792] 18.7 7.7
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 4.2
## Marotta15 2.8600 [0.8533; 9.5862] 0.2 2.2
## Deng16 1.5800 [1.3973; 1.7866] 19.6 7.7
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 3.0
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.2 2.4
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.1 1.5
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 0.4 3.6
## Ahrens22 2.1000 [1.0127; 4.3546] 0.6 4.1
## Qu24 1.2800 [1.1701; 1.4002] 36.7 7.8
## Chen25_mult 2.0900 [1.1543; 3.7841] 0.8 4.9
## Li26_mult 1.9100 [1.3912; 2.6222] 2.9 6.7
## Parada27_mult 0.8000 [0.5583; 1.1464] 2.3 6.4
## stro 1.4100 [1.0805; 1.8400] 4.2 7.0
## Duan31_mult 1.5700 [1.1493; 2.1447] 3.0 6.7
##
## Number of studies: k = 19
##
## OR 95%-CI z p-value
## Common effect model 1.2902 [1.2219; 1.3623] 9.18 < 0.0001
## Random effects model 1.3312 [1.0776; 1.6446] 2.65 0.0080
##
## Quantifying heterogeneity:
## tau^2 = 0.1473 [0.0622; 0.5378]; tau = 0.3838 [0.2495; 0.7334]
## I^2 = 77.8% [65.8%; 85.6%]; H = 2.12 [1.71; 2.63]
##
## Test of heterogeneity:
## Q d.f. p-value
## 81.08 18 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
# average OR
meta_a_analysis_remove <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = meta_data_a_remove,
sm = "OR"
)
summary(meta_a_analysis_remove)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.8950 [0.7079; 1.1316] 5.4 7.7
## Morgan3 0.7600 [0.4471; 1.2917] 1.1 5.1
## Tse9_mult 1.7700 [1.1655; 2.6881] 1.7 6.0
## Loperz10_mult 1.5200 [0.9089; 2.5419] 1.1 5.2
## Trabert11 1.0400 [0.9172; 1.1792] 18.8 8.4
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 3.9
## Marotta15 2.8600 [0.8533; 9.5862] 0.2 1.8
## Deng16 1.5800 [1.3973; 1.7866] 19.7 8.4
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 2.6
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.2 2.0
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.1 1.2
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 0.4 3.2
## Ahrens22 2.1000 [1.0127; 4.3546] 0.6 3.7
## Qu24 1.2800 [1.1701; 1.4002] 36.9 8.6
## Chen25_mult 2.0700 [1.1061; 3.8738] 0.8 4.4
## Li26_mult 1.1800 [0.8472; 1.6434] 2.7 6.8
## Parada27_mult 0.7680 [0.5351; 1.1022] 2.3 6.6
## Jia28 1.4100 [1.0805; 1.8400] 4.2 7.4
## Duan31_mult 1.4730 [1.0750; 2.0183] 3.0 7.0
##
## Number of studies: k = 19
##
## OR 95%-CI z p-value
## Common effect model 1.2547 [1.1882; 1.3250] 8.16 < 0.0001
## Random effects model 1.2328 [1.0255; 1.4822] 2.23 0.0259
##
## Quantifying heterogeneity:
## tau^2 = 0.1007 [0.0421; 0.4776]; tau = 0.3173 [0.2053; 0.6911]
## I^2 = 74.8% [60.5%; 83.9%]; H = 1.99 [1.59; 2.49]
##
## Test of heterogeneity:
## Q d.f. p-value
## 71.29 18 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
# Forest plot
# strong effect of OR
# pdf(file = "forestplot_strongeffect.pdf", width = 12, height = 10), use to save the forest plot
forest(meta_s_analysis_remove,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
# average OR
# pdf(file = "forestplot_average.pdf", width = 12, height = 10)
forest(meta_a_analysis_remove,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
# dev.off(), use to save the forest plot
Assess the publication bias of general meta analysis
# Funnel plot
# strong effect of OR
# pdf(file = "funnelplot_strongeffect.pdf", width = 12, height = 10)
funnel(meta_s_analysis_remove)
# average OR
# pdf(file = "funnelplot_average.pdf", width = 12, height = 10)
funnel(meta_a_analysis_remove)
# dev.off()
# assess the asymmetry of funnel plot and publication bias
# Conduct the meta-analysis using rma() function from metafor
# strong effect of OR
meta_s_analysis_rma <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = meta_data_s_remove)
# Perform Egger's test for publication bias
eggers_test_s <- regtest(meta_s_analysis_rma, model = "lm")
# Output the results of Egger's test
summary(meta_s_analysis_rma)
##
## Random-Effects Model (k = 19; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## -14.0124 28.0248 32.0248 33.8055 32.8248
##
## tau^2 (estimated amount of total heterogeneity): 0.1473 (SE = 0.0696)
## tau (square root of estimated tau^2 value): 0.3838
## I^2 (total heterogeneity / total variability): 89.29%
## H^2 (total variability / sampling variability): 9.34
##
## Test for Heterogeneity:
## Q(df = 18) = 81.0760, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.2861 0.1079 2.6526 0.0080 0.0747 0.4975 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(eggers_test_s$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -3.6143 -2.1381 0.5684 1.5165 3.3439
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.23185 0.09063 2.558 0.0204 *
## Xsei 0.25441 0.74939 0.339 0.7384
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.176 on 17 degrees of freedom
## Multiple R-squared: 0.5131, Adjusted R-squared: 0.4558
## F-statistic: 8.958 on 2 and 17 DF, p-value: 0.002203
# average OR
meta_a_analysis_rma <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = meta_data_a_remove)
# Perform Egger's test for publication bias
eggers_test_a <- regtest(meta_a_analysis_rma, model = "lm")
# Output the results of Egger's test
summary(meta_a_analysis_rma)
##
## Random-Effects Model (k = 19; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## -12.7095 25.4189 29.4189 31.1997 30.2189
##
## tau^2 (estimated amount of total heterogeneity): 0.1007 (SE = 0.0517)
## tau (square root of estimated tau^2 value): 0.3173
## I^2 (total heterogeneity / total variability): 85.00%
## H^2 (total variability / sampling variability): 6.67
##
## Test for Heterogeneity:
## Q(df = 18) = 71.2902, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.2093 0.0940 2.2274 0.0259 0.0251 0.3935 *
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(eggers_test_a$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -3.2693 -1.7941 0.3362 1.4424 3.6321
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.23617 0.08501 2.778 0.0129 *
## Xsei -0.10277 0.70154 -0.146 0.8853
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.047 on 17 degrees of freedom
## Multiple R-squared: 0.4838, Adjusted R-squared: 0.4231
## F-statistic: 7.966 on 2 and 17 DF, p-value: 0.003623
# Begg's Test
# strong effect of OR
begg_test_s <- ranktest(meta_s_analysis_rma)
print(begg_test_s)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.0409, p = 0.8360
# average OR
begg_test_a <- ranktest(meta_a_analysis_rma)
print(begg_test_a)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.0760, p = 0.6787
# Trim and Fill Method
# strong effect of OR
trimfill_result_s <- trimfill(meta_s_analysis_rma, estimator = "R0")
print(trimfill_result_s)
##
## Estimated number of missing studies on the left side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the left side: p-val = 0.5000
##
## Random-Effects Model (k = 19; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.1473 (SE = 0.0696)
## tau (square root of estimated tau^2 value): 0.3838
## I^2 (total heterogeneity / total variability): 89.29%
## H^2 (total variability / sampling variability): 9.34
##
## Test for Heterogeneity:
## Q(df = 18) = 81.0760, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.2861 0.1079 2.6526 0.0080 0.0747 0.4975 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# average OR
trimfill_result_a <- trimfill(meta_a_analysis_rma, estimator = "R0")
print(trimfill_result_a)
##
## Estimated number of missing studies on the left side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the left side: p-val = 0.5000
##
## Random-Effects Model (k = 19; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.1007 (SE = 0.0517)
## tau (square root of estimated tau^2 value): 0.3173
## I^2 (total heterogeneity / total variability): 85.00%
## H^2 (total variability / sampling variability): 6.67
##
## Test for Heterogeneity:
## Q(df = 18) = 71.2902, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.2093 0.0940 2.2274 0.0259 0.0251 0.3935 *
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Part 2, subgroup region, China vs None-China
# subgroup - nation
# strong effect OR
meta_data_s_na <- meta_data_s_remove %>%
mutate(
region_code = ifelse(region == "China", 0, 1)
)
meta_s_analysis_china <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_s_na, region_code == "0"), # China
sm = "OR"
)
meta_s_analysis_other <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_s_na, region_code == "1"), # other region
sm = "OR"
)
summary(meta_s_analysis_china)
## OR 95%-CI %W(common) %W(random)
## Tse9_mult 1.8800 [1.2379; 2.8551] 2.4 10.8
## Zhang14 0.3800 [0.1888; 0.7650] 0.9 6.9
## Deng16 1.5800 [1.3973; 1.7866] 28.0 15.3
## Zhou17 3.5700 [1.3702; 9.3013] 0.5 4.6
## Qu24 1.2800 [1.1701; 1.4002] 52.5 15.6
## Chen25_mult 2.0900 [1.1543; 3.7841] 1.2 8.2
## Li26_mult 1.9100 [1.3912; 2.6222] 4.2 12.5
## stro 1.4100 [1.0805; 1.8400] 6.0 13.4
## Duan31_mult 1.5700 [1.1493; 2.1447] 4.3 12.6
##
## Number of studies: k = 9
##
## OR 95%-CI z p-value
## Common effect model 1.4145 [1.3254; 1.5095] 10.45 < 0.0001
## Random effects model 1.5121 [1.1851; 1.9294] 3.33 0.0009
##
## Quantifying heterogeneity:
## tau^2 = 0.0970 [0.0360; 1.1774]; tau = 0.3115 [0.1897; 1.0851]
## I^2 = 75.3% [52.3%; 87.2%]; H = 2.01 [1.45; 2.79]
##
## Test of heterogeneity:
## Q d.f. p-value
## 32.35 8 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_s_analysis_other)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.9500 [0.7479; 1.2067] 17.2 15.9
## Morgan3 0.7600 [0.4471; 1.2917] 3.5 11.4
## Loperz10_mult 2.3100 [1.4284; 3.7357] 4.3 12.2
## Trabert11 1.0400 [0.9172; 1.1792] 62.3 17.2
## Marotta15 2.8600 [0.8533; 9.5862] 0.7 4.6
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.7 5.0
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.4 3.1
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 1.5 7.7
## Ahrens22 2.1000 [1.0127; 4.3546] 1.8 8.7
## Parada27_mult 0.8000 [0.5583; 1.1464] 7.6 14.2
##
## Number of studies: k = 10
##
## OR 95%-CI z p-value
## Common effect model 1.0417 [0.9433; 1.1503] 0.81 0.4200
## Random effects model 1.1417 [0.8446; 1.5433] 0.86 0.3889
##
## Quantifying heterogeneity:
## tau^2 = 0.1334 [0.0159; 0.7626]; tau = 0.3653 [0.1259; 0.8733]
## I^2 = 61.1% [22.5%; 80.5%]; H = 1.60 [1.14; 2.27]
##
## Test of heterogeneity:
## Q d.f. p-value
## 23.16 9 0.0058
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_s_analysis_remove)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.9500 [0.7479; 1.2067] 5.2 7.2
## Morgan3 0.7600 [0.4471; 1.2917] 1.1 5.3
## Tse9_mult 1.8800 [1.2379; 2.8551] 1.7 6.0
## Loperz10_mult 2.3100 [1.4284; 3.7357] 1.3 5.6
## Trabert11 1.0400 [0.9172; 1.1792] 18.7 7.7
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 4.2
## Marotta15 2.8600 [0.8533; 9.5862] 0.2 2.2
## Deng16 1.5800 [1.3973; 1.7866] 19.6 7.7
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 3.0
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.2 2.4
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.1 1.5
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 0.4 3.6
## Ahrens22 2.1000 [1.0127; 4.3546] 0.6 4.1
## Qu24 1.2800 [1.1701; 1.4002] 36.7 7.8
## Chen25_mult 2.0900 [1.1543; 3.7841] 0.8 4.9
## Li26_mult 1.9100 [1.3912; 2.6222] 2.9 6.7
## Parada27_mult 0.8000 [0.5583; 1.1464] 2.3 6.4
## stro 1.4100 [1.0805; 1.8400] 4.2 7.0
## Duan31_mult 1.5700 [1.1493; 2.1447] 3.0 6.7
##
## Number of studies: k = 19
##
## OR 95%-CI z p-value
## Common effect model 1.2902 [1.2219; 1.3623] 9.18 < 0.0001
## Random effects model 1.3312 [1.0776; 1.6446] 2.65 0.0080
##
## Quantifying heterogeneity:
## tau^2 = 0.1473 [0.0622; 0.5378]; tau = 0.3838 [0.2495; 0.7334]
## I^2 = 77.8% [65.8%; 85.6%]; H = 2.12 [1.71; 2.63]
##
## Test of heterogeneity:
## Q d.f. p-value
## 81.08 18 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
# average OR
meta_data_a_na <- meta_data_a_remove %>%
mutate(
region_code = ifelse(region == "China", 0, 1)
)
meta_a_analysis_china <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_a_na, region_code == "0"), # China
sm = "OR"
)
meta_a_analysis_other <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_a_na, region_code == "1"), # other region
sm = "OR"
)
summary(meta_a_analysis_china)
## OR 95%-CI %W(common) %W(random)
## Tse9_mult 1.7700 [1.1655; 2.6881] 2.4 10.0
## Zhang14 0.3800 [0.1888; 0.7650] 0.9 5.4
## Deng16 1.5800 [1.3973; 1.7866] 28.2 17.8
## Zhou17 3.5700 [1.3702; 9.3013] 0.5 3.3
## Qu24 1.2800 [1.1701; 1.4002] 52.8 18.5
## Chen25_mult 2.0700 [1.1061; 3.8738] 1.1 6.3
## Li26_mult 1.1800 [0.8472; 1.6434] 3.9 12.2
## Jia28 1.4100 [1.0805; 1.8400] 6.0 14.0
## Duan31_mult 1.4730 [1.0750; 2.0183] 4.3 12.6
##
## Number of studies: k = 9
##
## OR 95%-CI z p-value
## Common effect model 1.3801 [1.2930; 1.4731] 9.68 < 0.0001
## Random effects model 1.4006 [1.1574; 1.6949] 3.46 0.0005
##
## Quantifying heterogeneity:
## tau^2 = 0.0492 [0.0273; 1.1477]; tau = 0.2218 [0.1652; 1.0713]
## I^2 = 71.6% [44.1%; 85.6%]; H = 1.88 [1.34; 2.64]
##
## Test of heterogeneity:
## Q d.f. p-value
## 28.22 8 0.0004
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_a_analysis_other)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.8950 [0.7079; 1.1316] 17.9 21.8
## Morgan3 0.7600 [0.4471; 1.2917] 3.5 9.0
## Loperz10_mult 1.5200 [0.9089; 2.5419] 3.7 9.4
## Trabert11 1.0400 [0.9172; 1.1792] 62.3 28.9
## Marotta15 2.8600 [0.8533; 9.5862] 0.7 2.2
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.7 2.4
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.4 1.4
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 1.5 4.5
## Ahrens22 2.1000 [1.0127; 4.3546] 1.8 5.5
## Parada27_mult 0.7680 [0.5351; 1.1022] 7.5 14.8
##
## Number of studies: k = 10
##
## OR 95%-CI z p-value
## Common effect model 1.0068 [0.9118; 1.1117] 0.13 0.8933
## Random effects model 1.0134 [0.8409; 1.2212] 0.14 0.8891
##
## Quantifying heterogeneity:
## tau^2 = 0.0272 [0.0000; 0.6208]; tau = 0.1649 [0.0000; 0.7879]
## I^2 = 43.6% [0.0%; 72.9%]; H = 1.33 [1.00; 1.92]
##
## Test of heterogeneity:
## Q d.f. p-value
## 15.94 9 0.0680
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_a_analysis_remove)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.8950 [0.7079; 1.1316] 5.4 7.7
## Morgan3 0.7600 [0.4471; 1.2917] 1.1 5.1
## Tse9_mult 1.7700 [1.1655; 2.6881] 1.7 6.0
## Loperz10_mult 1.5200 [0.9089; 2.5419] 1.1 5.2
## Trabert11 1.0400 [0.9172; 1.1792] 18.8 8.4
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 3.9
## Marotta15 2.8600 [0.8533; 9.5862] 0.2 1.8
## Deng16 1.5800 [1.3973; 1.7866] 19.7 8.4
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 2.6
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.2 2.0
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.1 1.2
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 0.4 3.2
## Ahrens22 2.1000 [1.0127; 4.3546] 0.6 3.7
## Qu24 1.2800 [1.1701; 1.4002] 36.9 8.6
## Chen25_mult 2.0700 [1.1061; 3.8738] 0.8 4.4
## Li26_mult 1.1800 [0.8472; 1.6434] 2.7 6.8
## Parada27_mult 0.7680 [0.5351; 1.1022] 2.3 6.6
## Jia28 1.4100 [1.0805; 1.8400] 4.2 7.4
## Duan31_mult 1.4730 [1.0750; 2.0183] 3.0 7.0
##
## Number of studies: k = 19
##
## OR 95%-CI z p-value
## Common effect model 1.2547 [1.1882; 1.3250] 8.16 < 0.0001
## Random effects model 1.2328 [1.0255; 1.4822] 2.23 0.0259
##
## Quantifying heterogeneity:
## tau^2 = 0.1007 [0.0421; 0.4776]; tau = 0.3173 [0.2053; 0.6911]
## I^2 = 74.8% [60.5%; 83.9%]; H = 1.99 [1.59; 2.49]
##
## Test of heterogeneity:
## Q d.f. p-value
## 71.29 18 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
# Forest plot
# strong effect of OR
#pdf(file = "forestplot_strongeffect_china.pdf", width = 12, height = 10)
forest(meta_s_analysis_china,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
#pdf(file = "forestplot_strongeffect_otherregion.pdf", width = 12, height = 10)
forest(meta_s_analysis_other,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
# average OR
#pdf(file = "forestplot_average_china.pdf", width = 12, height = 10)
forest(meta_a_analysis_china,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
#pdf(file = "forestplot_average_otherregion.pdf", width = 12, height = 10)
forest(meta_a_analysis_other,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
#dev.off()
Assess the publication bias of subgroup - China
# Funnel plot
# strong effect of OR
# pdf(file = "funnelplot_strongeffect_china.pdf", width = 12, height = 10)
funnel(meta_s_analysis_china)
# pdf(file = "funnelplot_strongeffect_otherregion.pdf", width = 12, height = 10)
funnel(meta_s_analysis_other)
# average OR
# pdf(file = "funnelplot_average_china.pdf", width = 12, height = 10)
funnel(meta_a_analysis_china)
# pdf(file = "funnelplot_average_otherregion.pdf", width = 12, height = 10)
funnel(meta_a_analysis_other)
# dev.off()
# assess the asymmetry of funnel plot and publication bias
# Conduct the meta-analysis using rma() function from metafor
# strong effect of OR
meta_s_analysis_rma_china <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_s_na, region_code == "0"))
# Perform Egger's test for publication bias
eggers_test_s_china <- regtest(meta_s_analysis_rma_china, model = "lm")
# Output the results of Egger's test
summary(eggers_test_s_china$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -4.3260 -0.3764 0.6767 1.2026 1.9604
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.2829 0.1095 2.583 0.0363 *
## Xsei 0.8230 1.1004 0.748 0.4789
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.069 on 7 degrees of freedom
## Multiple R-squared: 0.7884, Adjusted R-squared: 0.728
## F-statistic: 13.04 on 2 and 7 DF, p-value: 0.004355
# average OR
meta_a_analysis_rma_china <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_a_na, region_code == "0"))
# Perform Egger's test for publication bias
eggers_test_a_china <- regtest(meta_a_analysis_rma_china, model = "lm")
# Output the results of Egger's test
summary(eggers_test_a_china$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -3.8134 -1.0655 0.2727 1.0738 2.2181
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.3023 0.1055 2.867 0.0241 *
## Xsei 0.2560 1.0565 0.242 0.8154
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.999 on 7 degrees of freedom
## Multiple R-squared: 0.7706, Adjusted R-squared: 0.705
## F-statistic: 11.76 on 2 and 7 DF, p-value: 0.005784
# Begg's Test
# strong effect of OR
begg_test_s_china <- ranktest(meta_s_analysis_rma_china)
print(begg_test_s_china)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.1111, p = 0.7614
# average OR
begg_test_a_china <- ranktest(meta_a_analysis_rma_china)
print(begg_test_a_china)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.1667, p = 0.6122
# Trim and Fill Method
# strong effect of OR
trimfill_result_s_china <- trimfill(meta_s_analysis_rma_china, estimator = "R0")
summary(trimfill_result_s_china)
##
## Estimated number of missing studies on the left side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the left side: p-val = 0.5000
##
## Random-Effects Model (k = 9; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## -5.9479 11.8957 15.8957 16.0546 18.2957
##
## tau^2 (estimated amount of total heterogeneity): 0.0970 (SE = 0.0672)
## tau (square root of estimated tau^2 value): 0.3115
## I^2 (total heterogeneity / total variability): 87.54%
## H^2 (total variability / sampling variability): 8.03
##
## Test for Heterogeneity:
## Q(df = 8) = 32.3466, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.4135 0.1243 3.3260 0.0009 0.1698 0.6572 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# average OR
trimfill_result_a_china <- trimfill(meta_a_analysis_rma_china, estimator = "R0")
summary(trimfill_result_a_china)
##
## Estimated number of missing studies on the left side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the left side: p-val = 0.5000
##
## Random-Effects Model (k = 9; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## -5.6519 11.3038 15.3038 15.4627 17.7038
##
## tau^2 (estimated amount of total heterogeneity): 0.0492 (SE = 0.0400)
## tau (square root of estimated tau^2 value): 0.2218
## I^2 (total heterogeneity / total variability): 77.88%
## H^2 (total variability / sampling variability): 4.52
##
## Test for Heterogeneity:
## Q(df = 8) = 28.2157, p-val = 0.0004
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.3369 0.0973 3.4618 0.0005 0.1461 0.5276 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Assess the publication bias of subgroup - other region
# assess the asymmetry of funnel plot and publication bias
# Conduct the meta-analysis using rma() function from metafor
# strong effect of OR
meta_s_analysis_rma_other <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_a_na, region_code == "1"))
# Perform Egger's test for publication bias
eggers_test_s_other <- regtest(meta_s_analysis_rma_other, model = "lm")
# Output the results of Egger's test
summary(eggers_test_s_other$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -1.6470 -1.1947 0.1187 1.2256 1.7021
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt -0.04115 0.10455 -0.394 0.704
## Xsei 0.40244 0.65356 0.616 0.555
##
## Residual standard error: 1.379 on 8 degrees of freedom
## Multiple R-squared: 0.04633, Adjusted R-squared: -0.1921
## F-statistic: 0.1943 on 2 and 8 DF, p-value: 0.8272
# average OR
meta_a_analysis_rma_other <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_a_na, region_code == "0"))
# Perform Egger's test for publication bias
eggers_test_a_other <- regtest(meta_a_analysis_rma_other, model = "lm")
# Output the results of Egger's test
summary(eggers_test_a_other$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -3.8134 -1.0655 0.2727 1.0738 2.2181
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.3023 0.1055 2.867 0.0241 *
## Xsei 0.2560 1.0565 0.242 0.8154
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.999 on 7 degrees of freedom
## Multiple R-squared: 0.7706, Adjusted R-squared: 0.705
## F-statistic: 11.76 on 2 and 7 DF, p-value: 0.005784
# Begg's Test
# strong effect of OR
begg_test_s_other <- ranktest(meta_s_analysis_rma_other)
begg_test_s_other
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.1556, p = 0.6007
# average OR
begg_test_a_other <- ranktest(meta_a_analysis_rma_other)
begg_test_a_other
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.1667, p = 0.6122
# Trim and Fill Method
# strong effect of OR
trimfill_result_s_other <- trimfill(meta_s_analysis_rma_other, estimator = "R0")
trimfill_result_s_other
##
## Estimated number of missing studies on the left side: 1 (SE = 2.0000)
## Test of H0: no missing studies on the left side: p-val = 0.2500
##
## Random-Effects Model (k = 11; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0313 (SE = 0.0388)
## tau (square root of estimated tau^2 value): 0.1770
## I^2 (total heterogeneity / total variability): 41.56%
## H^2 (total variability / sampling variability): 1.71
##
## Test for Heterogeneity:
## Q(df = 10) = 19.0183, p-val = 0.0400
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## -0.0090 0.0977 -0.0925 0.9263 -0.2005 0.1825
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# average OR
trimfill_result_a_other <- trimfill(meta_a_analysis_rma_other, estimator = "R0")
trimfill_result_a_other
##
## Estimated number of missing studies on the left side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the left side: p-val = 0.5000
##
## Random-Effects Model (k = 9; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0492 (SE = 0.0400)
## tau (square root of estimated tau^2 value): 0.2218
## I^2 (total heterogeneity / total variability): 77.88%
## H^2 (total variability / sampling variability): 4.52
##
## Test for Heterogeneity:
## Q(df = 8) = 28.2157, p-val = 0.0004
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.3369 0.0973 3.4618 0.0005 0.1461 0.5276 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Part 3, subgroup study design, cross sectional vs case control
# re-code the data
# strong effect of OR
meta_data_s_sen <- meta_data_s_remove %>%
mutate(
study_design = factor(study_design, levels = c(0, 1), labels = c("case-control", "cross-sectional"))
)
# average OR
meta_data_a_sen <- meta_data_a_remove %>%
mutate(
study_design = factor(study_design, levels = c(0, 1), labels = c("case-control", "cross-sectional"))
)
# strong effect of OR
# case control study
meta_s_analysis_cc <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_s_sen, study_design == "case-control"),
sm = "OR"
)
# cross sectional study
meta_s_analysis_cs <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_s_sen, study_design == "cross-sectional"),
sm = "OR"
)
# average OR
# case control study
meta_a_analysis_cc <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_a_sen, study_design == "case-control"),
sm = "OR"
)
# cross sectional study
meta_a_analysis_cs <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_a_sen, study_design == "cross-sectional"),
sm = "OR"
)
# Summary of the meta-analysis
# strong effect of OR
summary(meta_s_analysis_cc)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.9500 [0.7479; 1.2067] 5.3 8.5
## Tse9_mult 1.8800 [1.2379; 2.8551] 1.7 7.1
## Loperz10_mult 2.3100 [1.4284; 3.7357] 1.3 6.5
## Trabert11 1.0400 [0.9172; 1.1792] 19.1 9.1
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 4.9
## Deng16 1.5800 [1.3973; 1.7866] 20.0 9.1
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 3.4
## Ahrens22 2.1000 [1.0127; 4.3546] 0.6 4.7
## Qu24 1.2800 [1.1701; 1.4002] 37.5 9.3
## Chen25_mult 2.0900 [1.1543; 3.7841] 0.9 5.6
## Li26_mult 1.9100 [1.3912; 2.6222] 3.0 7.9
## Parada27_mult 0.8000 [0.5583; 1.1464] 2.3 7.6
## stro 1.4100 [1.0805; 1.8400] 4.3 8.3
## Duan31_mult 1.5700 [1.1493; 2.1447] 3.1 7.9
##
## Number of studies: k = 14
##
## OR 95%-CI z p-value
## Common effect model 1.2999 [1.2304; 1.3734] 9.36 < 0.0001
## Random effects model 1.3978 [1.1185; 1.7467] 2.94 0.0032
##
## Quantifying heterogeneity:
## tau^2 = 0.1375 [0.0620; 0.6616]; tau = 0.3707 [0.2490; 0.8134]
## I^2 = 81.9% [70.7%; 88.8%]; H = 2.35 [1.85; 2.99]
##
## Test of heterogeneity:
## Q d.f. p-value
## 71.69 13 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_s_analysis_cs)
## OR 95%-CI %W(common) %W(random)
## Morgan3 0.7600 [0.4471; 1.2917] 51.5 37.1
## Marotta15 2.8600 [0.8533; 9.5862] 9.9 14.1
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 11.0 15.3
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 6.0 9.4
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 21.5 24.1
##
## Number of studies: k = 5
##
## OR 95%-CI z p-value
## Common effect model 0.8991 [0.6143; 1.3158] -0.55 0.5840
## Random effects model 0.9869 [0.5876; 1.6574] -0.05 0.9601
##
## Quantifying heterogeneity:
## tau^2 = 0.1152 [0.0000; 2.9306]; tau = 0.3394 [0.0000; 1.7119]
## I^2 = 31.7% [0.0%; 73.9%]; H = 1.21 [1.00; 1.96]
##
## Test of heterogeneity:
## Q d.f. p-value
## 5.86 4 0.2102
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_s_analysis_remove)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.9500 [0.7479; 1.2067] 5.2 7.2
## Morgan3 0.7600 [0.4471; 1.2917] 1.1 5.3
## Tse9_mult 1.8800 [1.2379; 2.8551] 1.7 6.0
## Loperz10_mult 2.3100 [1.4284; 3.7357] 1.3 5.6
## Trabert11 1.0400 [0.9172; 1.1792] 18.7 7.7
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 4.2
## Marotta15 2.8600 [0.8533; 9.5862] 0.2 2.2
## Deng16 1.5800 [1.3973; 1.7866] 19.6 7.7
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 3.0
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.2 2.4
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.1 1.5
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 0.4 3.6
## Ahrens22 2.1000 [1.0127; 4.3546] 0.6 4.1
## Qu24 1.2800 [1.1701; 1.4002] 36.7 7.8
## Chen25_mult 2.0900 [1.1543; 3.7841] 0.8 4.9
## Li26_mult 1.9100 [1.3912; 2.6222] 2.9 6.7
## Parada27_mult 0.8000 [0.5583; 1.1464] 2.3 6.4
## stro 1.4100 [1.0805; 1.8400] 4.2 7.0
## Duan31_mult 1.5700 [1.1493; 2.1447] 3.0 6.7
##
## Number of studies: k = 19
##
## OR 95%-CI z p-value
## Common effect model 1.2902 [1.2219; 1.3623] 9.18 < 0.0001
## Random effects model 1.3312 [1.0776; 1.6446] 2.65 0.0080
##
## Quantifying heterogeneity:
## tau^2 = 0.1473 [0.0622; 0.5378]; tau = 0.3838 [0.2495; 0.7334]
## I^2 = 77.8% [65.8%; 85.6%]; H = 2.12 [1.71; 2.63]
##
## Test of heterogeneity:
## Q d.f. p-value
## 81.08 18 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
# average OR
summary(meta_a_analysis_cc)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.8950 [0.7079; 1.1316] 5.5 8.9
## Tse9_mult 1.7700 [1.1655; 2.6881] 1.7 6.9
## Loperz10_mult 1.5200 [0.9089; 2.5419] 1.1 5.9
## Trabert11 1.0400 [0.9172; 1.1792] 19.2 9.9
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 4.4
## Deng16 1.5800 [1.3973; 1.7866] 20.1 9.9
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 2.9
## Ahrens22 2.1000 [1.0127; 4.3546] 0.6 4.1
## Qu24 1.2800 [1.1701; 1.4002] 37.6 10.1
## Chen25_mult 2.0700 [1.1061; 3.8738] 0.8 4.9
## Li26_mult 1.1800 [0.8472; 1.6434] 2.8 7.9
## Parada27_mult 0.7680 [0.5351; 1.1022] 2.3 7.5
## Jia28 1.4100 [1.0805; 1.8400] 4.3 8.6
## Duan31_mult 1.4730 [1.0750; 2.0183] 3.1 8.1
##
## Number of studies: k = 14
##
## OR 95%-CI z p-value
## Common effect model 1.2635 [1.1958; 1.3350] 8.33 < 0.0001
## Random effects model 1.2757 [1.0528; 1.5458] 2.49 0.0130
##
## Quantifying heterogeneity:
## tau^2 = 0.0932 [0.0431; 0.5927]; tau = 0.3053 [0.2076; 0.7699]
## I^2 = 79.2% [65.7%; 87.3%]; H = 2.19 [1.71; 2.81]
##
## Test of heterogeneity:
## Q d.f. p-value
## 62.43 13 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_a_analysis_cs)
## OR 95%-CI %W(common) %W(random)
## Morgan3 0.7600 [0.4471; 1.2917] 51.5 37.1
## Marotta15 2.8600 [0.8533; 9.5862] 9.9 14.1
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 11.0 15.3
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 6.0 9.4
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 21.5 24.1
##
## Number of studies: k = 5
##
## OR 95%-CI z p-value
## Common effect model 0.8991 [0.6143; 1.3158] -0.55 0.5840
## Random effects model 0.9869 [0.5876; 1.6574] -0.05 0.9601
##
## Quantifying heterogeneity:
## tau^2 = 0.1152 [0.0000; 2.9306]; tau = 0.3394 [0.0000; 1.7119]
## I^2 = 31.7% [0.0%; 73.9%]; H = 1.21 [1.00; 1.96]
##
## Test of heterogeneity:
## Q d.f. p-value
## 5.86 4 0.2102
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_a_analysis_remove)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.8950 [0.7079; 1.1316] 5.4 7.7
## Morgan3 0.7600 [0.4471; 1.2917] 1.1 5.1
## Tse9_mult 1.7700 [1.1655; 2.6881] 1.7 6.0
## Loperz10_mult 1.5200 [0.9089; 2.5419] 1.1 5.2
## Trabert11 1.0400 [0.9172; 1.1792] 18.8 8.4
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 3.9
## Marotta15 2.8600 [0.8533; 9.5862] 0.2 1.8
## Deng16 1.5800 [1.3973; 1.7866] 19.7 8.4
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 2.6
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.2 2.0
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.1 1.2
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 0.4 3.2
## Ahrens22 2.1000 [1.0127; 4.3546] 0.6 3.7
## Qu24 1.2800 [1.1701; 1.4002] 36.9 8.6
## Chen25_mult 2.0700 [1.1061; 3.8738] 0.8 4.4
## Li26_mult 1.1800 [0.8472; 1.6434] 2.7 6.8
## Parada27_mult 0.7680 [0.5351; 1.1022] 2.3 6.6
## Jia28 1.4100 [1.0805; 1.8400] 4.2 7.4
## Duan31_mult 1.4730 [1.0750; 2.0183] 3.0 7.0
##
## Number of studies: k = 19
##
## OR 95%-CI z p-value
## Common effect model 1.2547 [1.1882; 1.3250] 8.16 < 0.0001
## Random effects model 1.2328 [1.0255; 1.4822] 2.23 0.0259
##
## Quantifying heterogeneity:
## tau^2 = 0.1007 [0.0421; 0.4776]; tau = 0.3173 [0.2053; 0.6911]
## I^2 = 74.8% [60.5%; 83.9%]; H = 1.99 [1.59; 2.49]
##
## Test of heterogeneity:
## Q d.f. p-value
## 71.29 18 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
# Forest plot
# strong effect of OR
#pdf(file = "forestplot_strongeffect_cc.pdf", width = 12, height = 10)
forest(meta_s_analysis_cc,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
#pdf(file = "forestplot_strongeffect_cs.pdf", width = 12, height = 10)
forest(meta_s_analysis_cs,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
# average OR
#pdf(file = "forestplot_average_cc.pdf", width = 12, height = 10)
forest(meta_a_analysis_cc,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
#pdf(file = "forestplot_average_cs.pdf", width = 12, height = 10)
forest(meta_a_analysis_cs,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
#dev.off()
# Funnel plot
# strong effect of OR
#pdf(file = "fuunelplot_strongeffect_cc.pdf", width = 12, height = 10)
funnel(meta_s_analysis_cc)
#pdf(file = "fuunelplot_strongeffect_cs.pdf", width = 12, height = 10)
funnel(meta_s_analysis_cs)
# average OR
#pdf(file = "fuunelplot_average_cc.pdf", width = 12, height = 10)
funnel(meta_a_analysis_cc)
#pdf(file = "fuunelplot_average_cs.pdf", width = 12, height = 10)
funnel(meta_s_analysis_cs)
#dev.off()
Assess the publication bias subgroup study design, case control
# assess the asymmetry of funnel plot and publication bias
# Conduct the meta-analysis using rma() function from metafor
# strong effect of OR
meta_s_analysis_rma_cc <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_s_sen, study_design == "case-control"))
# Perform Egger's test for publication bias
eggers_test_s_cc <- regtest(meta_s_analysis_rma_cc, model = "lm")
# Output the results of Egger's test
summary(eggers_test_s_cc$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -4.0165 -2.0335 0.7715 1.4064 3.3622
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.1999 0.1114 1.795 0.0979 .
## Xsei 0.7462 1.0617 0.703 0.4956
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.395 on 12 degrees of freedom
## Multiple R-squared: 0.5676, Adjusted R-squared: 0.4955
## F-statistic: 7.876 on 2 and 12 DF, p-value: 0.006536
# average OR
meta_a_analysis_rma_cc <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_a_sen, study_design == "case-control"))
# Perform Egger's test for publication bias
eggers_test_a_cc <- regtest(meta_a_analysis_rma_cc, model = "lm")
# Output the results of Egger's test
summary(eggers_test_a_cc$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -3.4464 -2.1832 0.6999 1.4205 3.6008
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.2251 0.1054 2.135 0.0541 .
## Xsei 0.1054 1.0034 0.105 0.9181
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.28 on 12 degrees of freedom
## Multiple R-squared: 0.5267, Adjusted R-squared: 0.4478
## F-statistic: 6.676 on 2 and 12 DF, p-value: 0.01125
# Begg's Test
# strong effect of OR
begg_test_s_cc <- ranktest(meta_s_analysis_rma_cc)
print(begg_test_s_cc)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.1429, p = 0.5183
# average OR
begg_test_a_cc <- ranktest(meta_a_analysis_rma_cc)
print(begg_test_a_cc)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.2088, p = 0.3308
# Trim and Fill Method
# strong effect of OR
trimfill_result_s_cc <- trimfill(meta_s_analysis_rma_cc, estimator = "R0")
print(trimfill_result_s_cc)
##
## Estimated number of missing studies on the left side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the left side: p-val = 0.5000
##
## Random-Effects Model (k = 14; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.1375 (SE = 0.0693)
## tau (square root of estimated tau^2 value): 0.3707
## I^2 (total heterogeneity / total variability): 91.25%
## H^2 (total variability / sampling variability): 11.43
##
## Test for Heterogeneity:
## Q(df = 13) = 71.6923, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.3349 0.1137 2.9448 0.0032 0.1120 0.5578 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# average OR
trimfill_result_a_cc <- trimfill(meta_a_analysis_rma_cc, estimator = "R0")
print(trimfill_result_a_cc)
##
## Estimated number of missing studies on the left side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the left side: p-val = 0.5000
##
## Random-Effects Model (k = 14; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0932 (SE = 0.0507)
## tau (square root of estimated tau^2 value): 0.3053
## I^2 (total heterogeneity / total variability): 87.55%
## H^2 (total variability / sampling variability): 8.03
##
## Test for Heterogeneity:
## Q(df = 13) = 62.4297, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.2435 0.0980 2.4851 0.0130 0.0515 0.4355 *
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Assess the publication bias subgroup study design, cross
sectional
# assess the asymmetry of funnel plot and publication bias
# Conduct the meta-analysis using rma() function from metafor
# strong effect of OR
meta_s_analysis_rma_cs <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_s_sen, study_design == "cross-sectional"))
# Perform Egger's test for publication bias
eggers_test_s_cs <- regtest(meta_s_analysis_rma_cs, model = "lm")
# Output the results of Egger's test
summary(eggers_test_s_cs$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## 1 2 3 4 5
## 0.35744 1.18034 0.04209 -0.41607 -1.16380
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt -0.9129 0.5236 -1.744 0.180
## Xsei 2.0019 1.2051 1.661 0.195
##
## Residual standard error: 1.008 on 3 degrees of freedom
## Multiple R-squared: 0.5045, Adjusted R-squared: 0.1741
## F-statistic: 1.527 on 2 and 3 DF, p-value: 0.3488
# average OR
meta_a_analysis_rma_cs <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_a_sen, study_design == "cross-sectional"))
# Perform Egger's test for publication bias
eggers_test_a_cs <- regtest(meta_a_analysis_rma_cs, model = "lm")
# Output the results of Egger's test
summary(eggers_test_a_cs$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## 1 2 3 4 5
## 0.35744 1.18034 0.04209 -0.41607 -1.16380
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt -0.9129 0.5236 -1.744 0.180
## Xsei 2.0019 1.2051 1.661 0.195
##
## Residual standard error: 1.008 on 3 degrees of freedom
## Multiple R-squared: 0.5045, Adjusted R-squared: 0.1741
## F-statistic: 1.527 on 2 and 3 DF, p-value: 0.3488
# Begg's Test
# strong effect of OR
begg_test_s_cs <- ranktest(meta_s_analysis_rma_cs)
print(begg_test_s_cs)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.4000, p = 0.4833
# average OR
begg_test_a_cs <- ranktest(meta_a_analysis_rma_cs)
print(begg_test_a_cs)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.4000, p = 0.4833
# Trim and Fill Method
# strong effect of OR
trimfill_result_s_cs <- trimfill(meta_s_analysis_rma_cs, estimator = "R0")
print(trimfill_result_s_cs)
##
## Estimated number of missing studies on the left side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the left side: p-val = 0.5000
##
## Random-Effects Model (k = 5; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.1152 (SE = 0.2439)
## tau (square root of estimated tau^2 value): 0.3394
## I^2 (total heterogeneity / total variability): 33.57%
## H^2 (total variability / sampling variability): 1.51
##
## Test for Heterogeneity:
## Q(df = 4) = 5.8560, p-val = 0.2102
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## -0.0132 0.2645 -0.0500 0.9601 -0.5317 0.5052
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# average OR
trimfill_result_a_cs <- trimfill(meta_a_analysis_rma_cs, estimator = "R0")
print(trimfill_result_a_cs)
##
## Estimated number of missing studies on the left side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the left side: p-val = 0.5000
##
## Random-Effects Model (k = 5; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.1152 (SE = 0.2439)
## tau (square root of estimated tau^2 value): 0.3394
## I^2 (total heterogeneity / total variability): 33.57%
## H^2 (total variability / sampling variability): 1.51
##
## Test for Heterogeneity:
## Q(df = 4) = 5.8560, p-val = 0.2102
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## -0.0132 0.2645 -0.0500 0.9601 -0.5317 0.5052
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Part 4, subgroup sample method, urine (= 1) vs other (= 0, 2, and
3)
# re-code the data
# strong effect of OR
meta_data_s_sm <- meta_data_s_remove %>%
mutate(
samplemethod_code = ifelse(sample_method %in% c("1", "2"), 1, 0) # urine = 1, other = 0
)
# average OR
meta_data_a_sm <- meta_data_a_remove %>%
mutate(
samplemethod_code = ifelse(sample_method %in% c("1", "2"), 1, 0) # urine = 1, other = 0
)
# strong effect of OR, urine = 1, other = 0
# urine sample method
meta_s_analysis_ur <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_s_sm, samplemethod_code == "1"),
sm = "OR"
)
# other sample method
meta_s_analysis_ot <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_s_sm, samplemethod_code == "0"),
sm = "OR"
)
# average OR, urine = 1, other = 0
# urine sample method
meta_a_analysis_ur <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_a_sm, samplemethod_code == "1"),
sm = "OR"
)
# other sample method
meta_a_analysis_ot <- metagen(
TE = log_odds_ratio,
seTE = se_log_odds_ratio,
studlab = paste(auther),
data = subset(meta_data_a_sm, samplemethod_code == "0"),
sm = "OR"
)
# Summary of the meta-analysis
# strong effect of OR
summary(meta_s_analysis_ur)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.9500 [0.7479; 1.2067] 5.3 8.1
## Morgan3 0.7600 [0.4471; 1.2917] 1.1 6.0
## Loperz10_mult 2.3100 [1.4284; 3.7357] 1.3 6.4
## Trabert11 1.0400 [0.9172; 1.1792] 19.2 8.7
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 4.9
## Deng16 1.5800 [1.3973; 1.7866] 20.1 8.7
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 3.5
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.2 2.8
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.1 1.8
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 0.5 4.2
## Qu24 1.2800 [1.1701; 1.4002] 37.7 8.8
## Chen25_mult 2.0900 [1.1543; 3.7841] 0.9 5.6
## Li26_mult 1.9100 [1.3912; 2.6222] 3.0 7.6
## Parada27_mult 0.8000 [0.5583; 1.1464] 2.3 7.3
## stro 1.4100 [1.0805; 1.8400] 4.3 8.0
## Duan31_mult 1.5700 [1.1493; 2.1447] 3.1 7.7
##
## Number of studies: k = 16
##
## OR 95%-CI z p-value
## Common effect model 1.2761 [1.2078; 1.3484] 8.68 < 0.0001
## Random effects model 1.2482 [0.9921; 1.5705] 1.89 0.0585
##
## Quantifying heterogeneity:
## tau^2 = 0.1539 [0.0628; 0.6127]; tau = 0.3924 [0.2505; 0.7828]
## I^2 = 79.8% [68.1%; 87.3%]; H = 2.23 [1.77; 2.80]
##
## Test of heterogeneity:
## Q d.f. p-value
## 74.43 15 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_s_analysis_ot)
## OR 95%-CI %W(common) %W(random)
## Tse9_mult 1.8800 [1.2379; 2.8551] 69.1 69.1
## Marotta15 2.8600 [0.8533; 9.5862] 8.2 8.2
## Ahrens22 2.1000 [1.0127; 4.3546] 22.7 22.7
##
## Number of studies: k = 3
##
## OR 95%-CI z p-value
## Common effect model 1.9956 [1.4101; 2.8243] 3.90 < 0.0001
## Random effects model 1.9956 [1.4101; 2.8243] 3.90 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 = 0 [0.0000; 1.6115]; tau = 0 [0.0000; 1.2694]
## I^2 = 0.0% [0.0%; 89.6%]; H = 1.00 [1.00; 3.10]
##
## Test of heterogeneity:
## Q d.f. p-value
## 0.44 2 0.8036
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_s_analysis_remove)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.9500 [0.7479; 1.2067] 5.2 7.2
## Morgan3 0.7600 [0.4471; 1.2917] 1.1 5.3
## Tse9_mult 1.8800 [1.2379; 2.8551] 1.7 6.0
## Loperz10_mult 2.3100 [1.4284; 3.7357] 1.3 5.6
## Trabert11 1.0400 [0.9172; 1.1792] 18.7 7.7
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 4.2
## Marotta15 2.8600 [0.8533; 9.5862] 0.2 2.2
## Deng16 1.5800 [1.3973; 1.7866] 19.6 7.7
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 3.0
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.2 2.4
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.1 1.5
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 0.4 3.6
## Ahrens22 2.1000 [1.0127; 4.3546] 0.6 4.1
## Qu24 1.2800 [1.1701; 1.4002] 36.7 7.8
## Chen25_mult 2.0900 [1.1543; 3.7841] 0.8 4.9
## Li26_mult 1.9100 [1.3912; 2.6222] 2.9 6.7
## Parada27_mult 0.8000 [0.5583; 1.1464] 2.3 6.4
## stro 1.4100 [1.0805; 1.8400] 4.2 7.0
## Duan31_mult 1.5700 [1.1493; 2.1447] 3.0 6.7
##
## Number of studies: k = 19
##
## OR 95%-CI z p-value
## Common effect model 1.2902 [1.2219; 1.3623] 9.18 < 0.0001
## Random effects model 1.3312 [1.0776; 1.6446] 2.65 0.0080
##
## Quantifying heterogeneity:
## tau^2 = 0.1473 [0.0622; 0.5378]; tau = 0.3838 [0.2495; 0.7334]
## I^2 = 77.8% [65.8%; 85.6%]; H = 2.12 [1.71; 2.63]
##
## Test of heterogeneity:
## Q d.f. p-value
## 81.08 18 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
# average OR
summary(meta_a_analysis_ur)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.8950 [0.7079; 1.1316] 5.5 8.8
## Morgan3 0.7600 [0.4471; 1.2917] 1.1 5.7
## Loperz10_mult 1.5200 [0.9089; 2.5419] 1.2 5.8
## Trabert11 1.0400 [0.9172; 1.1792] 19.3 9.7
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 4.3
## Deng16 1.5800 [1.3973; 1.7866] 20.2 9.7
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 2.8
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.2 2.2
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.1 1.3
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 0.5 3.5
## Qu24 1.2800 [1.1701; 1.4002] 37.8 9.9
## Chen25_mult 2.0700 [1.1061; 3.8738] 0.8 4.8
## Li26_mult 1.1800 [0.8472; 1.6434] 2.8 7.7
## Parada27_mult 0.7680 [0.5351; 1.1022] 2.3 7.4
## Jia28 1.4100 [1.0805; 1.8400] 4.3 8.4
## Duan31_mult 1.4730 [1.0750; 2.0183] 3.1 7.9
##
## Number of studies: k = 16
##
## OR 95%-CI z p-value
## Common effect model 1.2414 [1.1748; 1.3118] 7.68 < 0.0001
## Random effects model 1.1566 [0.9561; 1.3992] 1.50 0.1343
##
## Quantifying heterogeneity:
## tau^2 = 0.0933 [0.0371; 0.5100]; tau = 0.3055 [0.1927; 0.7141]
## I^2 = 76.9% [62.7%; 85.7%]; H = 2.08 [1.64; 2.64]
##
## Test of heterogeneity:
## Q d.f. p-value
## 64.84 15 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_a_analysis_ot)
## OR 95%-CI %W(common) %W(random)
## Tse9_mult 1.7700 [1.1655; 2.6881] 69.1 69.1
## Marotta15 2.8600 [0.8533; 9.5862] 8.2 8.2
## Ahrens22 2.1000 [1.0127; 4.3546] 22.7 22.7
##
## Number of studies: k = 3
##
## OR 95%-CI z p-value
## Common effect model 1.9142 [1.3526; 2.7090] 3.66 0.0002
## Random effects model 1.9142 [1.3526; 2.7090] 3.66 0.0002
##
## Quantifying heterogeneity:
## tau^2 = 0 [0.0000; 2.0963]; tau = 0 [0.0000; 1.4479]
## I^2 = 0.0% [0.0%; 89.6%]; H = 1.00 [1.00; 3.10]
##
## Test of heterogeneity:
## Q d.f. p-value
## 0.62 2 0.7333
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
summary(meta_a_analysis_remove)
## OR 95%-CI %W(common) %W(random)
## Wu2_multi 0.8950 [0.7079; 1.1316] 5.4 7.7
## Morgan3 0.7600 [0.4471; 1.2917] 1.1 5.1
## Tse9_mult 1.7700 [1.1655; 2.6881] 1.7 6.0
## Loperz10_mult 1.5200 [0.9089; 2.5419] 1.1 5.2
## Trabert11 1.0400 [0.9172; 1.1792] 18.8 8.4
## Zhang14 0.3800 [0.1888; 0.7650] 0.6 3.9
## Marotta15 2.8600 [0.8533; 9.5862] 0.2 1.8
## Deng16 1.5800 [1.3973; 1.7866] 19.7 8.4
## Zhou17 3.5700 [1.3702; 9.3013] 0.3 2.6
## Morgan20_cervical 1.3300 [0.4216; 4.1957] 0.2 2.0
## Morgan20_ovarian 1.4100 [0.2984; 6.6632] 0.1 1.2
## Morgan20_uterine 0.5700 [0.2509; 1.2948] 0.4 3.2
## Ahrens22 2.1000 [1.0127; 4.3546] 0.6 3.7
## Qu24 1.2800 [1.1701; 1.4002] 36.9 8.6
## Chen25_mult 2.0700 [1.1061; 3.8738] 0.8 4.4
## Li26_mult 1.1800 [0.8472; 1.6434] 2.7 6.8
## Parada27_mult 0.7680 [0.5351; 1.1022] 2.3 6.6
## Jia28 1.4100 [1.0805; 1.8400] 4.2 7.4
## Duan31_mult 1.4730 [1.0750; 2.0183] 3.0 7.0
##
## Number of studies: k = 19
##
## OR 95%-CI z p-value
## Common effect model 1.2547 [1.1882; 1.3250] 8.16 < 0.0001
## Random effects model 1.2328 [1.0255; 1.4822] 2.23 0.0259
##
## Quantifying heterogeneity:
## tau^2 = 0.1007 [0.0421; 0.4776]; tau = 0.3173 [0.2053; 0.6911]
## I^2 = 74.8% [60.5%; 83.9%]; H = 1.99 [1.59; 2.49]
##
## Test of heterogeneity:
## Q d.f. p-value
## 71.29 18 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
# Forest plot
# strong effect of OR
#pdf(file = "forestplot_strongeffect_ur.pdf", width = 12, height = 10)
forest(meta_s_analysis_ur,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
#pdf(file = "forestplot_strongeffect_ot.pdf", width = 12, height = 10)
forest(meta_s_analysis_ot,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
# average OR
#pdf(file = "forestplot_average_ur.pdf", width = 12, height = 10)
forest(meta_a_analysis_ur,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
#pdf(file = "forestplot_average_ot.pdf", width = 12, height = 10)
forest(meta_a_analysis_ot,
sortvar = TE,
prediction = TRUE,
leftlabs = c("Author", "g", "SE")
)
#dev.off()
# Funnel plot
# strong effect of OR
#pdf(file = "fuunelplot_strongeffect_ur.pdf", width = 12, height = 10)
funnel(meta_s_analysis_ur)
#pdf(file = "fuunelplot_strongeffect_ot.pdf", width = 12, height = 10)
funnel(meta_s_analysis_ot)
# average OR
#pdf(file = "fuunelplot_average_ur.pdf", width = 12, height = 10)
funnel(meta_a_analysis_ur)
#pdf(file = "fuunelplot_average_ot.pdf", width = 12, height = 10)
funnel(meta_s_analysis_ot)
#dev.off()
Assess the publication bias, subgroup sample method, urine (=
1)
# assess the asymmetry of funnel plot and publication bias
# Conduct the meta-analysis using rma() function from metafor
# strong effect of OR
meta_s_analysis_rma_ur <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_s_sm, samplemethod_code == "1"))
# Perform Egger's test for publication bias
eggers_test_s_ur <- regtest(meta_s_analysis_rma_ur, model = "lm")
# Output the results of Egger's test
summary(eggers_test_s_ur$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -3.2773 -1.9511 0.2315 1.8617 3.3520
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.25686 0.09948 2.582 0.0217 *
## Xsei -0.15264 0.88524 -0.172 0.8656
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.303 on 14 degrees of freedom
## Multiple R-squared: 0.5041, Adjusted R-squared: 0.4332
## F-statistic: 7.115 on 2 and 14 DF, p-value: 0.007379
# average OR
meta_a_analysis_rma_ur <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_a_sm, samplemethod_code == "1"))
# Perform Egger's test for publication bias
eggers_test_a_ur <- regtest(meta_a_analysis_rma_ur, model = "lm")
# Output the results of Egger's test
summary(eggers_test_a_ur$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -2.9566 -1.6262 0.3912 1.2152 3.6340
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.26683 0.09089 2.936 0.0109 *
## Xsei -0.59362 0.80732 -0.735 0.4743
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.112 on 14 degrees of freedom
## Multiple R-squared: 0.496, Adjusted R-squared: 0.424
## F-statistic: 6.889 on 2 and 14 DF, p-value: 0.008259
# Begg's Test
# strong effect of OR
begg_test_s_ur <- ranktest(meta_s_analysis_rma_ur)
print(begg_test_s_ur)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.0000, p = 1.0000
# average OR
begg_test_a_ur <- ranktest(meta_a_analysis_rma_ur)
print(begg_test_a_ur)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 0.0000, p = 1.0000
# Trim and Fill Method
# strong effect of OR
trimfill_result_s_ur <- trimfill(meta_s_analysis_rma_ur, estimator = "R0")
print(trimfill_result_s_ur)
##
## Estimated number of missing studies on the right side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the right side: p-val = 0.5000
##
## Random-Effects Model (k = 16; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.1539 (SE = 0.0764)
## tau (square root of estimated tau^2 value): 0.3924
## I^2 (total heterogeneity / total variability): 90.96%
## H^2 (total variability / sampling variability): 11.06
##
## Test for Heterogeneity:
## Q(df = 15) = 74.4273, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.2217 0.1172 1.8922 0.0585 -0.0079 0.4514 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# average OR
trimfill_result_a_ur <- trimfill(meta_a_analysis_rma_ur, estimator = "R0")
print(trimfill_result_a_ur)
##
## Estimated number of missing studies on the right side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the right side: p-val = 0.5000
##
## Random-Effects Model (k = 16; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0933 (SE = 0.0512)
## tau (square root of estimated tau^2 value): 0.3055
## I^2 (total heterogeneity / total variability): 85.84%
## H^2 (total variability / sampling variability): 7.06
##
## Test for Heterogeneity:
## Q(df = 15) = 64.8440, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.1455 0.0972 1.4974 0.1343 -0.0449 0.3359
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Assess the publication bias, subgroup sample method, other (= 0, 2,
and 3)
# assess the asymmetry of funnel plot and publication bias
# Conduct the meta-analysis using rma() function from metafor
# strong effect of OR
meta_s_analysis_rma_ot <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_s_sm, samplemethod_code == "0"))
# Perform Egger's test for publication bias
eggers_test_s_ot <- regtest(meta_s_analysis_rma_ot, model = "lm")
# Output the results of Egger's test
summary(eggers_test_s_ot$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## 1 2 3
## 0.03285 0.06167 -0.09452
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.41922 0.05332 7.862 0.0805 .
## Xsei 0.96183 0.17374 5.536 0.1138
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1175 on 1 degrees of freedom
## Multiple R-squared: 0.9991, Adjusted R-squared: 0.9974
## F-statistic: 565.6 on 2 and 1 DF, p-value: 0.02972
# average OR
meta_a_analysis_rma_ot <- rma(yi = log_odds_ratio, sei = se_log_odds_ratio, method = "REML", data = subset(meta_data_a_sm, samplemethod_code == "0"))
# Perform Egger's test for publication bias
eggers_test_a_ot <- regtest(meta_a_analysis_rma_ot, model = "lm")
# Output the results of Egger's test
summary(eggers_test_a_ot$fit)
##
## Call:
## lm(formula = yi ~ X - 1, weights = 1/vi)
##
## Weighted Residuals:
## 1 2 3
## 0.01076 0.02020 -0.03096
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Xintrcpt 0.32079 0.01747 18.36 0.0346 *
## Xsei 1.16279 0.05691 20.43 0.0311 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0385 on 1 degrees of freedom
## Multiple R-squared: 0.9999, Adjusted R-squared: 0.9997
## F-statistic: 4738 on 2 and 1 DF, p-value: 0.01027
# Begg's Test
# strong effect of OR
begg_test_s_ot <- ranktest(meta_s_analysis_rma_ot)
print(begg_test_s_ot)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 1.0000, p = 0.3333
# average OR
begg_test_a_ot <- ranktest(meta_a_analysis_rma_ot)
print(begg_test_a_ot)
##
## Rank Correlation Test for Funnel Plot Asymmetry
##
## Kendall's tau = 1.0000, p = 0.3333
# Trim and Fill Method
# strong effect of OR
trimfill_result_s_ot <- trimfill(meta_s_analysis_rma_ot, estimator = "R0")
print(trimfill_result_s_ot)
##
## Estimated number of missing studies on the left side: 0 (SE = 1.4142)
## Test of H0: no missing studies on the left side: p-val = 0.5000
##
## Random-Effects Model (k = 3; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0 (SE = 0.1194)
## tau (square root of estimated tau^2 value): 0
## I^2 (total heterogeneity / total variability): 0.00%
## H^2 (total variability / sampling variability): 1.00
##
## Test for Heterogeneity:
## Q(df = 2) = 0.4372, p-val = 0.8036
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.6910 0.1772 3.8995 <.0001 0.3437 1.0382 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# average OR
trimfill_result_a_ot <- trimfill(meta_a_analysis_rma_ot, estimator = "R0")
print(trimfill_result_a_ot)
##
## Estimated number of missing studies on the left side: 1 (SE = 2.0000)
## Test of H0: no missing studies on the left side: p-val = 0.2500
##
## Random-Effects Model (k = 4; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0 (SE = 0.1109)
## tau (square root of estimated tau^2 value): 0
## I^2 (total heterogeneity / total variability): 0.00%
## H^2 (total variability / sampling variability): 1.00
##
## Test for Heterogeneity:
## Q(df = 3) = 1.1646, p-val = 0.7615
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.6132 0.1703 3.6007 0.0003 0.2794 0.9470 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1